The discovery of a new type of singular value, classified as ‘essential’, marked a turning point in the history of functions in the late 1860s, when the level of interest in infinite sets began to increase and questions multiplied. Once neglected and ostracized, singular values, and discontinuities in particular, became the driving force behind analysis. This reversal, together with sentiments against complex or negative numbers (see ch. 4), is indicative of the prejudices that were spreading in mathematics.